Question 22
Evaluate
$$15120\left(\frac2{1\times2\times3}+\frac3{1\times2\times3\times4}+\cdots+\frac6{1\times2\times3\times\cdots\times7}\right).$$
Answer format: enter one whole number without units; leading zeros are optional. The source answer sheet uses four digits (for example, 7 is shaded as 0007).
$$15120\left(\frac2{1\times2\times3}+\frac3{1\times2\times3\times4}+\cdots+\frac6{1\times2\times3\times\cdots\times7}\right).$$
Answer format: enter one whole number without units; leading zeros are optional. The source answer sheet uses four digits (for example, 7 is shaded as 0007).